1978 USAMO Problems/Problem 3

Problem

An integer $n$ will be called good if we can write

$n=a_1+a_2+\cdots+a_k$ ,

where $a_1,a_2, \ldots, a_k$ are positive integers (not necessarily distinct) satisfying

$\frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_k}=1$ .

Given the information that the integers 33 through 73 are good, prove that every integer $\ge 33$ is good.

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1978 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5
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